Example: Mandelbrot set

The Mandelbrot consists of points whose boundary is a two-dimensional fractal
shape. It is named after the mathematician Benoit Mandelbrot. It’s computed
using a lot of iterations, that’s why we use Lua here for the calculation.

The sampling is done via \addplot3 and the coloring by surf and shader=interp.
LuaTeX is required. And it runs a while. ;-)